Wave grooves on (ring) mesh
You could use the Simple Deform/Bend modifier:

Create your curve, use bezier curve if you want, then convert to mesh, use LoopTools &gt; Space to make the space between vertices regular:



Extrude up and down:



Give it the Simple Deform modifier, choose the Bend mode, bend 360° on the Z axis:



Keep a copy somewhere, apply the modifier:



Extrude inwards, merge the vertices by distance, delete the inner faces if you have some:



Bevel the curve, extrude inwards:



Give it a Subidivison Surface, add some edge loops to sharp the edges, etc...